Which of the following numbers is a multiple of 6? ${47,54,86,95,107}$
Solution: The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $47 \div 6 = 7\text{ R }5$ $54 \div 6 = 9$ $86 \div 6 = 14\text{ R }2$ $95 \div 6 = 15\text{ R }5$ $107 \div 6 = 17\text{ R }5$ The only answer choice that leaves no remainder after the division is $54$ $ 9$ $6$ $54$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $54$ $54 = 2\times3\times3\times3 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $54$. We can say that $54$ is divisible by $6$.